Hi and welcome to the forums!
for your CPU, no need to get an overkill of a graphics card, because the rest of your system is lacking. You won't be able to play BF4 well, but that's not beyond fixable (upgrade over time)
For your games, all you are going to need is a ATI Radeon HD 7770/Ghz, featuring 1GB GDDR5 Memory on a 128-bit bus, a very good graphics card for the price, avoid those DDR3 memory based graphics cards, you want GDDR5. Get this card now, and slowly incorporate/replace parts later. The reason why I don't suggest something overkill to utilize the full budget, is that it isn't necessary. This card draws very little power (80 watts max), so if you have over a 300W PSU, no matter of high quality, your PSU will be fine.
Get any of the 7770 brands like MSI/Sapphire or Asus